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A Global Perspective on Applied Mathematics & Numerical Analysis

机译:应用数学和数值分析的全球视角

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Mathematics has a great variety of applications in the physical sciences. This simple, undeniable fact, however, gives rise to an interesting philosophical problem: why should physical scientists find that they are unable to even state their theories without the resources of abstract mathematical theories? Moreover, the formulation of physical theories in the language of mathematics often leads to new physical predictions which were quite unexpected on purely physical grounds. It is thought by some that the puzzles the applications of mathematics present are artefacts of out-dated philosophical theories about the nature of mathematics. In this paper I examine numerical analysis what precisely it is and why it is important. I begin by presenting a selective conceptual reconstruction of one suggestive line in its historical development. Then expand my focus to a general account of what numerical analysis consists today.
机译:数学在物理科学中具有广泛的应用。但是,这个简单而不可否认的事实引起了一个有趣的哲学问题:为什么物理科学家会发现,如果没有抽象数学理论的资源,他们甚至无法陈述自己的理论?此外,用数学语言表述物理理论常常会导致新的物理预测,而这纯粹是基于物理的基础是出乎意料的。一些人认为,目前数学应用中的难题是关于数学性质的过时哲学理论的伪像。在本文中,我研究了数值分析的确切含义及其重要性。首先,我提出了一条暗示性路线在其历史发展中的选择性概念重建。然后将我的重点扩展到今天数值分析的一般说明。

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